1. Field of the Invention
The present invention relates to the prediction of the shape of a resist pattern formed by exposing and developing a resist.
2. Description of the Related Art
In lithography, a projection exposure apparatus transfers a reticle pattern onto a resist (photosensitive agent) applied on a substrate (e.g., a semiconductor wafer or glass plate), and a developing device develops the resist, thereby obtaining a resist pattern. The resist pattern shape can be measured using an SEM (scanning electron microscope).
Along with dramatic increases in the degree of integration of elements of semiconductor devices, their minimum line widths (design rules) are increasingly becoming shorter. Under the circumstances, the resolution is enhanced by shortening the wavelength of exposure light and increasing the numerical aperture of a projection optical system.
Unfortunately, such approaches to increasing the resolution cannot meet the required minimum line widths. To combat this shortcoming, a pattern correction technique using optical proximity effect is employed.
The pattern correction must be executed for the entire reticle pattern. For this reason, a reticle pattern correction operation takes a very long time.
Patent reference 1 and non-patent references 1 and 2 disclose methods of predicting the resist pattern shape by computing an aerial image, that is, light intensity distribution formed on a resist using a reticle pattern, and by determining the optical contour shape at an arbitrary light intensity level as the resist pattern shape. The computation accuracies of these prediction methods are relatively low due to approximation errors upon creating computation model equations.
Patent reference 2 computes the light intensity distribution of an aerial image formed on a resist using a reticle pattern. Based on the resultant light intensity distribution, an exponential decay function of two parameters, that is, a process factor and an edge light intensity shift is obtained. The convolution integral of the light intensity distribution and the exponential decay function is calculated, thereby computing the resist pattern shape. This method takes a long time to calculate the convolution integral.
[Patent Reference 1] U.S. Pat. No. 6,643,616
[Patent Reference 2] Japanese Patent Laid-Open No. 2000-58417
[Non-patent Reference 1] Mathematical and CAD Framework for Proximity Correction (1996 SPIE Vol. 2726 P 208-222, Optical Microlithography)
[Non-patent Reference 2] Experimental Results on Optical Proximity Correction with Variable Threshold Resist Model (1997 SPIE Vol. 3051 P 458-468, Optical Microlithography)